Theorem orim2d 793

Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 23-Apr-1995.)

Hypothesis

Ref	Expression
orim1d.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
orim2d	|- ( ph -> ( ( th \/ ps ) -> ( th \/ ch ) ) )

Proof of Theorem orim2d

Step	Hyp	Ref	Expression
1		idd 21	. 2 |- ( ph -> ( th -> th ) )
2		orim1d.1	. 2 |- ( ph -> ( ps -> ch ) )
3	1, 2	orim12d 791	1 |- ( ph -> ( ( th \/ ps ) -> ( th \/ ch ) ) )

Syntax hints:   -> wi 4   \/ wo 713

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 714

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim2  794  orbi2d  795  pm2.82  817  stdcndcOLD  851  pm2.13dc  890  exmid1dc  4283  acexmidlemcase  5995  poxp  6376  fodjuomnilemdc  7307  omniwomnimkv  7330  exmidontriimlem1  7399  indpi  7525  suplocexprlemloc  7904  nneoor  9545  uzp1  9752  maxabslemlub  11713  xrmaxiflemlub  11754  nninfctlemfo  12556  exmidunben  12992  bj-nn0suc  16285  sbthomlem  16352